High-Dimensional Copula Variational Approximation Through Transformation

• Activity Number: 454 - Computational Advances in Approximate Bayesian Methods
• Type: Topic Contributed
• Date/Time: Thursday, August 6, 2020 : 10:00 AM to 11:50 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Michael Smith* and Ruben Loaiza-Maya and David Nott
• Companies: University of Melbourne and Monash University and National University of Singapore
• Keywords: Factor variational approximation,; Inverse G&H transformation; Yeo-Johnson transformation; Implicit copula; skew-normal copula

Abstract

Variational methods are attractive for computing Bayesian inference when exact inference is impractical. They approximate a target distribution--either the posterior or an augmented posterior--using a simpler distribution that is selected to balance accuracy with computational feasibility. Here we approximate an element-wise parametric transformation of the target distribution as multivariate Gaussian or skew-normal. Approximations of this kind are implicit copula models for the original parameters, with a Gaussian or skew-normal copula function and flexible parametric margins. A key observation is that their adoption can improve the accuracy of variational inference in high dimensions at limited or no additional computational cost. We consider the Yeo-Johnson and inverse G&H transformations, along with sparse factor structures for the scale matrix of the Gaussian or skew-normal. We also show how to implement efficient re-parametrization gradient methods for these copula-based approximations. The efficacy of the approach is illustrated by computing posterior inference for different models using real datasets.